MENSAGEM PEDAGÓGICA EM TEXTOS DE MATERIAIS CURRICULARES EDUCATIVOS: uma análise a partir da dimensão organizacional

Nosso objetivo é identificar e caracterizar as variações na mensagem pedagógica que ocorrem na dimensão organizacional, no que diz respeito à prática pedagógica escolar representada em textos dos materiais curriculares educativos. O trabalho caracteriza-se por uma abordagem qualitativa, cujos dados foram produzidos por meio de documentos. A principal referência teórico-metodológica utilizada foi a teoria de Basil Bernstein. Em particular, foi utilizado o conceito de classificação, para analisar as relações entre discursos e espaços que são veiculados em textos desses materiais. Os resultados da análise mostraram que, além de motivos explícitos, a mensagem pedagógica em textos dos materiais curriculares educativos quanto à relação entre os espaços dos sujeitos, apresentou um partilhamento na organização e durante a realização da tarefa matemática, uma prática pedagógica escolar regulada por uma forte relação de intradisciplinaridade. Para isso, são empreendidos modos de ações de ensino que favorecem o sequenciamento da tarefa matemática.Palavras-chave: Mensagem pedagógica; Texto; Materiais curriculares educativos.Pedagogical message in texts of educational curriculum materials: an analysis based on the organizational dimensionAbstractWe aim to identify and characterize the variations in the pedagogical message which occur in the organizational dimension referring to the pedagogical practice represented in texts of educational curriculum materials. The work is characterized by a qualitative approach whose data were produced through documents. The main reference theoretical-methodological used was Basil Bernstein’s theory. In particular, it was used the concept of classification in order to analyze the relations among discourses and spaces that are transmitted in texts of these materials. The results of the analysis demonstrated that beyond explicit reasons, the pedagogical message in texts of educational curriculum materials referring to the subject’s spaces showed a sharing in the organization and during the realization of the mathematical task a school pedagogical practice regulated by a strong relation of intradisciplinarity. For this, modes of action are undertaken that favor the sequencing of the mathematical task.Key words: Pedagogical message; Text; Educational curriculum materials.Mensaje pedagógico en textos de materiales curriculares educativos: un análisis a partir de la dimensión organizacionalResumen Nuestro objetivo es identificar y caracterizar las variaciones en el mensaje pedagógico que ocurren en la dimensión organizacional, en lo que se refiere a la práctica pedagógica escolar representada en textos de los materiales curriculares educativos. El trabajo se caracteriza por un enfoque cualitativo, cuyos datos se han producido a través de documentos. La principal referencia teórico-metodológica utilizada fue la teoría de Basil Bernstein. En particular, se utilizó el concepto de clasificación, para analizar las relaciones entre discursos y espacios que se transmiten en textos de esos materiales. Los resultados del análisis mostraron que, además de motivos explícitos, el mensaje pedagógico en textos de los materiales curriculares educativos en cuanto a la relación entre los espacios de los sujetos, presentó un reparto en la organización y durante la realización de la tarea matemática, una práctica pedagógica escolar regulada por uma fuerte relación de intradisciplinaridad. Para ello, se emprenden modos de acciones de enseñanza que favorecen la secuenciación de la tarea matemática.Palabras clave: Mensaje pedagógico;. Texto; Materiales curriculares educativos.

Koneksi Matematis Siswa pada Tugas Matematis Berbasis Hasil Pertanian: Konteks, Konsep, dan Prosedur Matematis

The mathematical connection is a crucial ability possessed by vocational high school students in solving problems by their field of expertise. Agriculture is a field of expertise that requires a lot of mathematical connection skills to solve various problems. Increasing the ability of students' mathematical connections can be facilitated by the teacher by constructing mathematical tasks in the agricultural sector. This qualitative research using the case study method describes the construction of mathematical tasks based on agricultural products and the mathematical connection ability of students in solving the task. Mathematical task construction is carried out by integrating agricultural product contexts and mathematical concepts. The mathematical task was used in Grade X Agribusiness Expertise students of Agricultural Product Processing. Data retrieval of students' mathematical connection abilities was carried out through tests, observation results, answer sheets, and interviews that focused on connecting contexts with mathematical concepts, connections between mathematical concepts, and connections to mathematical procedures. The results of the student data analysis showed that the ability of mathematical connections was hampered by the ability of the connection between mathematical concepts. It is necessary to increase student's mathematical connections by constructing mathematical tasks with various mathematical concepts.

Different Perspectives on Success in Solving Stand-Alone Problems by 14 to 15-Year-Old Students / Različite prespektive o uspješnosti 14 i 15-godišnjaka u rješavanju izoliranoga problema

The paper defines a special type of problem tasks and considers its didactic potential, as well as the success of students in solving the selected problem. The research instrument used is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura). The geometrical task is presented in three versions: as a verbal problem, as a verbal problem with a corresponding image and as a problem in context. The material analysed in the present paper was collected from 182 students in 7th and 8th grade of Croatian urban elementary schools. The didactic potential is considered from the aspect of use of mathematical concepts and connections. The success of students in problem-solving is considered from the aspect of implementation of the problem-solving process and producing correct answers, depending on the manner in which the tasks are set up. The results show that the stand-alone problem, as a special type of problem task, has considerable didactic potential. However, the students’ skills of discovering and connecting mathematical concepts and their properties are underdeveloped. In addition, the manner in which the tasks are set up considerably affects the process of solving the task and consequently the success of that process. Based on the results of the research, proposals are given for application of stand-alone problems in teaching mathematics.Key words: isolated problem; mathematical task; problem solving; problem evaluation. --- U radu se definira posebna vrsta problemskoga zadatka te se razmatra njegov didaktički potencijal kao i uspješnost učenika u rješavanju odabranoga problema. Instrument istraživanja je geometrijski zadatak s državne mature koji se postavlja u tri inačice: kao tekstualni problem, kao tekstualni problem uz odgovarajuću sliku te kao zadatak u kontekstu. U istraživanju je sudjelovalo 182 učenika 7. i 8. razreda hrvatskih gradskih osnovnih škola. Didaktički potencijal razmatra se s aspekta iskoristivosti matematičkih koncepata i veza, a uspješnost učenika u rješavanju problema razmatra se s aspekta provedbe procesa rješavanja i otkrivanja točnoga rješenja ovisno o načinu postavljanja zadatka. Rezultati pokazuju da promatrani problem kao posebna vrsta problemskoga zadatka ima veliki didaktički potencijal, ali da učenici imaju nedovoljno razvijene vještine otkrivanja i povezivanja matematičkih koncepata i njihovih svojstava. Osim toga, način postavljanja zadatka značajno utječe na proces rješavanja, a posljedično i na uspješnost određivanja rješenja. Na temelju rezultata daju se prijedlozi primjene opisane vrste problema u nastavi Matematike.Ključne riječi: izolirani problem; matematički zadatak; rješavanje problema; vrednovanje problema

Breakfast and Exercise Improve Academic and Cognitive Performance in Adolescents

This study examined the combined effects of breakfast and exercise on short-term academic and cognitive performance in adolescents. Eighty-two adolescents (64 female), aged 14–19 years, were randomized to four groups over a 4-hour morning: (i) a group who fasted and were sedentary (F-S); (ii) a group who ate breakfast but were sedentary (B-S); (iii) a group who fasted but completed a 30-min exercise bout (F-E); and (iv) a group who ate breakfast and completed a 30-min exercise bout (B-E). Individuals completed academic and cognitive tests over the morning. Adolescents in B-E significantly improved their mathematics score (B-E: 15.2% improvement on correct answers, vs. F-S: 6.7% improvement on correct answers; p = 0.014) and computation time for correct answers (B-E: 16.7% improvement, vs. F-S: 7.4% improvement; p = 0.004) over the morning compared with the F-S group. The B-E group had faster reaction times for congruent, incongruent and control trials of the Stroop Color-Word Task compared with F-S mid-morning (all p < 0.05). Morning breakfast and exercise combine to improve short-term mathematical task performance and speed in adolescents.

A Comprehensive Analysis of Quantum Clustering : Finding All the Potential Minima

Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a σ value, a hyper-parameter which can be manually defined and manipulated to suit the application. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an outstanding task because normally such expressions are impossible to solve analytically. However, we prove that if the points are all included in a square region of size σ, there is only one minimum. This bound is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new numerical approach “per block”. This technique decreases the number of particles by approximating some groups of particles to weighted particles. These findings are not only useful to the quantum clustering problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics and other applications.

Mathematical Model of Spatial Motion of the Controlled Parachute-Tether System of the Wind Kite Type

Mathematical modeling is created for the mathematical task of spatial motion of the controlled parachute-tether system of the “wind kite” type. The mathematical model parachute-tether system consists of a model of the main parachute and a model of the braking parachute. The parachutes are connected by the tether. The model of the main parachute is supposed to be the solid body. This solid body has two planes of symmetry. The braking parachute is the solid body with axial symmetry. The tether model is an absolutely flexible elastic thread. The tether is connected by ideal hinges with the main parachute and braking parachute. The control of the main parachute is carried out by changing the length of the control slings. Changing the length causes deformation of the dome. This is the reason for the change in its aerodynamics. Maneuvering of the main parachute occurs in the vertical plane, when the length of the control slings changes simultaneously. Maneuvering of the main parachute in space is carried out when the length of the control slings changes, when the slings are given a travel difference. The system of dynamic and kinematic equations is designed for calculating the controlled spatial movement of the main parachute, braking parachute and tether. The option exists when the mass of the tether and the forces applied to the tether cannot be neglected. The motion of the tether is represented by the equations of motion of an absolutely flexible elastic thread in projections on the axis of a natural trihedron. The mathematical model is represented by a system of ordinary differential equations and partial differential equations. The problem is solved using various numerical methods. The solution is possible with the help of an integrated numerical and analytical approach as well.

Content and Structure of Psychological Readiness of Secondary School Students to Solve Creative Mathematical Tasks

Informational technologies, the latest challenges in the field of technical development of society condition irreversible environmental and human changes. In the context of these changes a special place is occupied by those activities that are directly or indirectly related to technical, cybernetic, mathematical activities. This actualizes the manifestation of mathematical abilities, giftedness for math activity in youth, features of creative potential, etc. The purpose of the study is to clarify the content and structure of psychological readiness of high school students for creative mathematical performance. The main content characteristics of the creative mathematical problem as a model for the study of creative mathematical activities are considered in the article. Based on the theory of learning problems, the psychological structure of mathematical task is determined. The structure contains the following components: a) the subject of the task (in its initial state or the ascending subject of the task); b) the model of desired state, ie the requirements (set and required) of the task. The contradiction of the creative mathematical situation first of all characterized by the object and subject of the creative mathematical task. The psychological readiness of high school students for creative mathematical performance is an integrated personality trait aimed at realizing of the cognitive abilities of young people in the process of solving creative mathematical problems. Since the process of creative mathematical thinking (creative mathematical activity) is determined by objective (subject-functional) and subjective-personal (motivation, emotional-volitional, value attitude) components, it is worth saying about subject-functional, subjective-personal types of psychological readiness of high school students to perform mathematical creative activities.

Mathematics in the Subject of Vegetable Processing Production

Mathematics studied in SMK should have relevance with student competencies to support vocational school education goals. This study aims to explore the role of mathematics in the Vegetable Processing Production Subject. This subject is studied by students of the Agricultural Product Processing Agribusiness Competency Vocational School. This research uses a qualitative approach. The role of mathematics in the production of vegetable processing is explored from the perspective of productive teachers and documents. The analysis to explore the role of mathematics and its relevance to mathematics content and mathematics learning. The results show that the role of mathematics is to calculate and measure the various needs for tools, materials, and business planning analysis for the production of vegetable processing. The role of mathematics has relevance to the mathematical content of numbers and measurements. The integration of vegetable product processing production contexts can be done to construct a mathematical concept or present a mathematical task situation as an effort to develop mathematical understanding by student expertise.